A Minimum-Elimination-Escape Function Method for Multimodal Optimization Problems

Auxiliary function method is an effective and practical approach for multimodal optimization problems, which is often troubled by "Mexican hat" effect. In this paper, a minimum-elimination-escape function is proposed for multimodal problems, which can avoid the troublesome effect and diminish the influence of local optimum. The proposed function is composed of two sub-functions: minimum-elimination function and minimum-escape function. The minimum-elimination function was used to flatten the initial problem so that the number of local optimum can be reduced. Then, the minimum-escape function is constructed for the flattened problem, which can convert the current minimal solution to the unique global maximum. At last, based on these two functions, an optimization method is designed. Experiments on 12 widely used benchmark are made. In experiments, influences of the parameter and initial points are analyzed. Comparisons with 8 existing methods indicate that the performance of the proposed algorithm is positive and effective.